ArticleOriginal scientific text

Title

On the disc-convexity of complex Banach manifolds

Authors 1, 1

Affiliations

  1. Department of Mathematics, Institute of Pedagogy of Hanoi 1, Cau giay, Tu liem, Ha noi, Vietnam

Abstract

The Banach hyperbolicity and disc-convexity of complex Banach manifolds and their relations are investigated.

Keywords

Banach manifold, hyperbolic, disc-convex

Bibliography

  1. R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc. 235 (1978), 213-219.
  2. K. Diederich and N. Sibony, Strange complex structures on Euclidean space, J. Reine Angew. Math. 311/312 (1979), 397-407.
  3. G. Fischer, Complex Analytic Geometry, Lecture Notes in Math. 538, Springer, 1976.
  4. A. Hirschowitz, Pseudoconvexité au-dessus d'espaces plus ou moins homogènes, Invent. Math. 26 (1974), 303-322.
  5. S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Dekker, 1970.
  6. S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357-416.
  7. S. Lang, Introduction to Complex Hyperbolic Spaces, Springer, 1987.
  8. P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 121, North-Holland, 1987.
  9. J. P. Ramis, Sous-ensembles Analytiques d'une Variété Banachique Complexe, Ergeb. Math. Grenzgeb. 53, Springer, 1970.
  10. B. Shabat, Introduction to Complex Analysis, Part II, Functions of Several Variables, Transl. Math. Monographs 110, Amer. Math. Soc., 1992.
  11. B. Shiffman, Extension of holomorphic maps into hermitian manifolds, Math. Ann. 194 (1971), 249-258.
  12. N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230.
  13. B. D. Tac, Extending holomorphic maps in infinite dimensions, Ann. Polon. Math. 54 (1991), 241-253.
  14. D. D. Thai, Royden-Kobayashi pseudometric and tautness of normalizations of complex spaces, Boll. Un. Mat. Ital. A (7) 5 (1991), 147-156.
  15. H. Toruńczyk, Smooth partitions of unity on some non-separable Banach spaces, Studia Math. 66 (1973), 44-51.
  16. T. Urata, The hyperbolicity of complex analytic spaces, Bull. Aichi Univ. of Education 31 (1982), 65-75.
  17. E. Vesentini, Invariant distances and invariant differential metrics in locally convex spaces, in: Spectral Theory, Banach Center Publ. 8, PWN-Polish Sci. Publ., Warszawa, 1982, 493-512.
  18. M. Zaĭdenberg, The Picard theorem and hyperbolicity, Siberian Math. J. 24 (1983), 858-867 (English transl.).
  19. M. Zaĭdenberg, S. Kreĭn, P. Kuchment and A. Pankov, Banach bundles and linear operators, Uspekhi Mat. Nauk 30 (1975), no. 5, 101-157 (in Russian).
Pages:
1-11
Main language of publication
English
Received
1994-07-07
Accepted
1996-04-20
Published
1998
Exact and natural sciences